Geometry: Perpendicular and Parallel Line Through a Given Point

Happy Wednesday math friends! Today we’re going to go over the difference between perpendicular and parallel lines. Then we’ll use our knowledge of equation of a line (y=mx+b) to see how to find perpendicular and parallel lines through a given point.  This is is a common question that comes up on the NYS Geometry Regents and is something we should prepare for, so let’s go!

If you need any further explanation, don’t hesitate to check out the Youtube video below that goes into detail on how to solve these types of questions one step at a time. Happy calculating! 🙂

Perpendicular lines: Lines that intersect to create a 90-degree angle and can look something like the graph below.  Their slopes are negative reciprocals of each other which means they are flipped and negated. See below for example!Screen Shot 2020-06-10 at 10.26.10 AM

Example: Find an equation of a line that passes through the point (1,3) and is perpendicular to line y=2x+1 .

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Parallel lines are lines that go in the same direction and have the same slope (but have different y-intercepts). Check out the example below!

Screen Shot 2020-06-10 at 10.29.26 AMExample: Find an equation of a line that goes through the point (-5,1) and is parallel to line y=4x+2.Screen Shot 2020-06-10 at 10.34.46 AMScreen Shot 2020-06-10 at 10.35.23 AMTry the following practice questions on your own!

Practice Questions:

1) Find an equation of a line that passes through the point (2,5) and is perpendicular to line y=2x+1.

 2) Find an equation of a line that goes through the point (-2,4) and is perpendicular to lineScreen Shot 2020-06-10 at 11.24.06 AM

 3)  Find an equation of a line that goes through the point (1,6) and is parallel to line y=3x+2.

4)  Find an equation of a line that goes through the point (-2,-2)  and is parallel to line y=2x+1.

Solutions:Screen Shot 2020-06-10 at 11.22.05 AM

Need more of an explanation? Check out the video that goes over these types of questions up on Youtube (video at top of post) and let me know if you have still any questions.

Happy Calculating! 🙂

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Geometry: Median of a Trapezoid Theorem

*If you haven’t done so, check out the video that goes over this exact problem, also please don’t forget to subscribe!

Medians of a Trapezoid copy

Screen Shot 2020-06-02 at 7.31.07 AMStep 1:  Let’s apply the Median of a Trapezoid Theorem to this question!  A little rusty?  No problem, check out the Theorem below.

Median of a Trapezoid Theorem: The median of a trapezoid is equal to the sum of both bases.Screen Shot 2020-06-02 at 7.32.31 AMStep 2: Now that we found the value of x , we can plug it back into the equation for Screen Shot 2020-06-02 at 7.33.44 AMmedian,  to find the value of median Screen Shot 2020-06-02 at 7.34.25 AM

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Want more practice?  Your wish is my command! Check out the practice problems below:

Practice Questions:

1.Screen Shot 2020-06-02 at 7.35.29 AMis the median of trapezoid ABCDEF, find the value of the median, given the following:Screen Shot 2020-06-02 at 7.35.47 AM2. Screen Shot 2020-06-02 at 9.01.08 AMis the median of trapezoid ACTIVE, find the value of the median, given the following:Screen Shot 2020-06-02 at 9.16.22 AM3.Screen Shot 2020-06-02 at 9.17.01 AMis the median of  trapezoid DRAGON, find the value of the median, given the following:Screen Shot 2020-06-02 at 9.22.13 AM

4. Screen Shot 2020-06-02 at 9.23.08 AMis the median of trapezoid MATRIX, find the value of the median, given the following:Screen Shot 2020-06-02 at 9.23.43 AM

Solutions:

Screen Shot 2020-06-02 at 9.25.05 AM

Need more of an explanation?  Check out the detailed video and practice problems. Happy calculating! 🙂

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Bored and Confused?

Calling all students, teachers, and parents!  As everyone is stuck at home during a global pandemic, now is a great time we are all forced to try and understand math (and our sanity level) a little bit more.  Well, I may not be able to help you with the keeping sanity stuff, but as far as math goes, hopefully, the below websites offer some much needed mathematic support.

All jokes aside I hope everyone is staying safe and successfully social distancing.  Stay well, math friends! 🙂

Kahn Academy: The same Kahn Academy we know and love still has amazing videos and tutorials as usual, but now they also have a live “homeroom” chat on Facebook LIVE every day at 12:00pm. The chats occur daily with Kahn Academy founder Sal and at times feature famous guests such as Bill Gates. Click the link below for more:

Khan Academy Homeroom Screen Shot 2020-04-04 at 12.21.20 PM

 

Study.com: In a time when companies are being more generous, Study.com is here for us as they offer up to 1000 licenses for school districts and free lessons for teachers, students, and parents.  Check out all the education freebies here:

Study.com

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Math PlanetIf you’re looking for free math resources in Pre-Algebra, Algebra, Algebra 2, and Geometry then you will find the answers you need at Math Planet.  All free all the time, find their website here:

MathPlanet 

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JMAP: For anyone who has to take the NYS Regents at some point (whenever we’re allowed to go outside again), JMAP has every old Regents exam as well as answers to boot! Did I mention each exam is free and printable?  Find their website here:

JMAP

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What is your favorite educational site?  Let me know in the comments, and stay well! 🙂

Geometry: The Voluminous “Vessel” at Hudson Yards

Calling all NYC dwellers! Have you seen the new structure at Hudson Yards?  A staircase to nowhere, this bee-hive like structure is for the true adventurists at heart; Clearly, I had to check it out!

Where does math come in here you say?  Well, during my exploration, I had to wonder (as am sure most people do) what is the volume of this structure?  What do you think the volume of the Vessel is? (Hint: feel free to approximate!)

Screen Shot 2019-04-11 at 5.38.46 PM.png

Solution: I estimated the volume by using the formula of a three-dimensional cone. (Not an exact measurement of the Vessel, but close enough!) .

Screen Shot 2019-04-11 at 5.08.42 PM Screen Shot 2019-04-12 at 1.20.08 PM.pngWe can find the radius and height based on the given information above.  Everything we need for our formula is right here!

Screen Shot 2019-04-14 at 4.49.16 PM

Now that we have our information, let’s fill in our formula and calculate! Screen Shot 2019-04-11 at 5.14.58 PM.pngScreen Shot 2019-04-11 at 5.17.30 PM.png

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Extra Tip! Notice that we labeled the solution with feet cubed Screen Shot 2019-04-14 at 4.53.49 PM.png, which is the short-handed way to write “feet cubed.”  Why feet cubed instead of feet squared? Or just plain old feet? When we use our formula we are multiplying three numbers all measured in feet:

radius X radius X (Height/3)

All three values are measured in feet! –> Feet cubed (Screen Shot 2019-04-14 at 4.53.49 PM.png)

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Did you get the same answer? Did you use a different method or have any questions?  Let me know in the comments and happy mathing! 🙂

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Summertime Review: Factoring

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Whether you are ready to go back to school or back to sleep, I hope you found this factoring review helpful.

Still got questions?  Don’t hesitate to reach out in the comments below! Happy math-ing! 🙂

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Simultaneous Equations/New YouTube Channel!

In need of a bit of review on Simultaneous Equations?  Well, now is your chance! Learn how to solve these confusing bad mama jamma’s in three different ways and choose which one works best for you!

I’m also excited to introduce my new YouTube page for MathSux!  Hope these new set of videos help.  Let me know if you have any more questions in the comments.  Happy calculating! 🙂

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